Drogba, who won the title last season with Chelsea, will take some cheer from his performance in Saturday's domestic championship game against Mersin Idman Yurdu when he scored two second-half goals in a 3-1 win.
However, the mood at Galatasaray was soured at that game by coach Fatih Terim's anger at refereeing decisions in a row which led to him and his two assistants being sent to the stands, overshadowing preparations for Tuesday's return leg in Istanbul.
In Madrid last week, Galatasaray were taught "a good lesson" by the Spanish side, according to Drogba.
"We're not at their level but I think it's a lack of experience more than anything else," Drogba told beIN Sport. "We're learning, we're a young team. There are things that need improving.
"It's a good lesson, and one we have to show we've learned well in the return leg. We wanted to contain Madrid but we could have done it in a different way, with more audacity and aggression. We could have caused them problems as we had chances but that's the way it is," he said.
One of Galatasaray's biggest headaches is the absence of key striker Burak Yilmaz, who is suspended after picking up a yellow card in Madrid.
Turkish media reported on Friday that the Istanbul side had applied to UEFA to have the yellow card annulled.
Galatasaray will also be missing central defender Dany Nounkeu after his booking in Madrid ruled him out.
Real romped to a 5-1 victory at home to mid-table Levante on Saturday as coach Jose Mourinho left several top performers, including forward Cristiano Ronaldo, out of his starting line-up.
Ronaldo came off the bench at half-time with Real leading 2-1 and netted his 29th goal of the La Liga campaign before setting up fellow substitute Mesut Ozil.
Centre-back Sergio Ramos and midfielder Xabi Alonso both played the full 90 minutes as they are suspended for Tuesday's game.
"It could be that we are in our best form of the season," Ronaldo, top scorer in the Champions League this season with nine goals, told reporters. "We have a complete squad with all the players available and that is very positive news."
On Tuesday's game in Istanbul, he added: "It's a tough match and our passage to the next round is not yet assured. Three goals is a big lead but we have to go there and play and at least get one goal.
"We have to take things step by step, game by game, but I think we have a good chance of getting to the final."
Galatasaray: 25-Fernando Muslera; 27-Emmanuel Eboue, 26-Semih Kaya, 11-Albert Riera, 53-Nordin Amrabat; 14-Wesley Sneijder, 10-Felipe Melo, 8-Selcuk Inan, 4-Hamit Altintop; 19-Umut Bulut, 12-Didier Drogba.
Real Madrid: 41-Diego Lopez; 17-Alvaro Arbeloa, 2-Raphael Varane, 3-Pepe, 5-Fabio Coentrao; 6-Sami Khedira, 19-Luka Modric; 22-Angel di Maria, 10-Mesut Ozil, 7-Cristiano Ronaldo; 9-Karim Benzema.
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